Photonic chip-based all-optical XOR gate for 40 and 160 Gbit/s DPSK signals

We demonstrate a photonic chip-based all-optical exclusive-OR (XOR) gate for phase-encoded optical signals via four-wave mixing in a highly nonlinear, dispersion-engineered chalcogenide (As2S3) planar waveguide. We achieve error-free, XOR operation for 40?Gbit/s differential phase shift keying (DPSK) optical signals with no power penalty. The effectiveness and broad bandwidth operation of our approach is highlighted by implementing an XOR gate for 160?Gbit/s DPSK signals.     

Surface-enhanced Raman effect in ultra-thin CuPc films employing periodic silver nanostructures

In order to investigate the interaction of organic molecules with metals by means of Raman spectroscopy, special substrates were designed which combine interference and surface-enhancement mechanisms. Triangular shaped silver nanostructures with an angle bisector and a height of about 80 nm were prepared by nanosphere lithography on silicon substrates with a 100-nm oxide layer. Utilizing these substrates the dependence of the Raman signal intensity on the thickness of copper phthalocyanine (CuPc) was studied in the range from few percentages of a monolayer coverage up to 80 nm using an in situ setup. At an excitation in resonance with the plasmons of the nanostructures (2.6 eV) an increase of the signal was observed during film growth. Contrary to that, excitation at 1.92 eV in resonance with the CuPc absorption band leads to a strongly enhanced Raman signal for submonolayer coverage which hardly changes with the CuPc film thickness in the ultra-low coverage regime.     

Fourier's law from Schrödinger dynamics

We consider a class of one-dimensional chains of weakly coupled many level systems. We present a theory which predicts energy diffusion within these chains for almost all initial states, if some concrete conditions on their Hamiltonians are met. By numerically solving the time dependent Schr?dinger equation, we verify this prediction. Close to equilibrium we analyze this behavior in terms of heat conduction and compute the respective coefficient directly from the theory.     

Well-posedness of non-autonomous linear evolution equations for generators whose commutators are scalar

We prove the well-posedness of non-autonomous linear evolution equations for generators \({A(t): D(A(t)) \subset X \to X}\) whose pairwise commutators are complex scalars, and in addition, we establish an explicit representation formula for the evolution. We also prove well-posedness in the more general case where instead of the onefold commutators only the p-fold commutators of the operators A(t) are complex scalars. All these results are furnished with rather mild stability and regularity assumptions: Indeed, stability in X and strong continuity conditions are sufficient. Additionally, we improve a well-posedness result of Kato for group generators A(t) by showing that the original norm continuity condition can be relaxed to strong continuity. Applications include Segal field operators and Schrödinger operators for particles in external electric fields.     

An efficient linear solver for the hybridized discontinuous Galerkin method

Discretizing partial differential equations by an implicit solving technique ultimately leads to a linear system of equations that has to be solved. The number of globally coupled unknowns is especially large for discontinuous Galerkin (DG) methods. It can be reduced by using hybridized discontinuous Galerkin (HDG) methods, but still efficient linear solvers are needed. It has been shown that, if hierarchical basis functions are used, a hierarchical scale separation (HSS) ansatz can be an efficient solver. In this work, we couple the HDG method with an HSS solver to solve a scalar nonlinear problem. It is validated by comparing the results with results obtained by GMRES with ILU(3) preconditioning as linear solver. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A dual algorithm for convex-concave data smoothing by cubicC 2-splines

Summary In this paper the problem of smoothing a given data set by cubicC ²-splines is discussed. The spline may required to be convex in some parts of the domain and concave in other parts. Application of splines has the advantage that the smoothing problem is easily discretized. Moreover, the special structure of the arising finite dimensional convex program allows a dualization such that the resulting concave dual program is unconstrained. Therefore the latter program is treated numerically much more easier than the original program. Further, the validity of a return-formula is of importance by which a minimizer of the orginal program is obtained from a maximizer of the dual program.The theoretical background of this general approach is discussed and, above all, the details for applying the strategy to the present smoothing problem are elaborated. Also some numerical tests are presented.     

Hypercyclic operators on non-locally convex spaces

We transfer a number of fundamental results about hypercyclic operators on locally convex spaces (due to Ansari, Bès, Bourdon, Costakis, Feldman, and Peris) to the non-locally convex situation. This answers a problem posed by A. Peris [Multi-hypercyclic operators are hypercyclic, Math. Z. 236 (2001), 779-786].

     

Resonant transition radiation in the X-ray region from a low emittance 855 MeV electron beam

The interference of transition radiation coherently produced from a periodic stack of four polyimide foils of 7.2 μm thickness and a separation of 162 μm was investigated. This stack has been brought into the low emittance (3 π nm rad) electron beam of the 855 MeV Mainz Microtron MAMI. Transition radiation was observed in the energy range from 2 to 15 keV with a LN₂-cooled pin photodiode. A good energy resolution of 0.8 keV and angular resolution of 0.15 mrad was achieved simultaneously allowing for the first time to quantitatively study the interference pattern. Good agreement with theoretical calculations is found. Prospects to exploit transition radiation in the x-ray region from a low emittance electron beam as a high brilliant radiation source are discussed.     

Continuity Properties of Integral Kernels Associated with Schrödinger Operators on Manifolds

For Schr?dinger operators (including those with magnetic fields) with singular scalar potentials on manifolds of bounded geometry, we study continuity properties of some related integral kernels: the heat kernel, the Green function, and also kernels of some other functions of the operator. In particular, we show the joint continuity of the heat kernel and the continuity of the Green function outside the diagonal. The proof makes intensive use of the Lippmann–Schwinger equation. Submitted: September 20, 2005. Revised: July 20, 2006. Accepted: October 31, 2006.     

On the Existence of Specific Stars in Planar Graphs

Given a graph G, a (k;a,b,c)-star in G is a subgraph isomorphic to a star K_1,3 with a central vertex of degree k and three leaves of degrees a, b and c in G. The main result of the paper is: Every planar graph G of minimum degree at least 3 contains a (k;a,b,c)-star with a≤ b≤ c and (i) k = 3, a≤ 10, or (ii) k = 4, a = 4, 4≤ b≤ 10, or (iii) k = 4, a = 5, 5≤ b≤ 9, or (iv) k = 4, 6≤ a≤ 7, 6≤ b≤ 8, or (v) k = 5, 4≤ a≤ 5, 5≤ b≤ 6 and 5≤ c≤ 7, or (vi) k = 5 and a = b = c = 6.